1. Field of the Invention
The present invention relates to a compound lens which is preferably used in small cameras, demultiplexers, multiplexers and optical fiber couplers in fields of optical information processing and optical communication, and furthermore in the field of medical industry.
2. Description of the Prior Art
As compound lenses in such fields, compound lenses of configurations which will be described hereinafter have been known heretofore.
In U.S. Pat. No. 4,208,088, there is, as shown in FIG. 1, proposed a compound lens 11 having three arrays arranged, each array consisting of sphere lens 21 having a homogeneous refractive index. In FIG. 1, the character O designates an object point and the character I an image point. The pulse-like line shown below the compound lens 11 is a graph illustrating an index distribution of the compound lens 11, and it is shown that the sphere lens 21 are optically homogeneous. This compound lens 11 is very low in resolution since the sphere lens 21 homogeneous in refractive index are large in spherical aberration.
Another earlier attempts are illustrated in FIGS. 2 and 3. In FIG. 2, the compound lens 12 has a structure such that optically homogeneous sphere lenses are replace by sphere lenses 22 which are spherically symmetric in index distribution (heterogeneous in refractive index) for reducing spherical aberration. The compound lens 13 of FIG. 3 has such a configuration that sphere lenses 21 are held between distributed index or gradient index planar lens 23.sub.1, 23.sub.2, 23.sub.3 and 23.sub.4. In FIG. 3, reference numerals 23.sub.1 ' to 23.sub.6 ' designate refractive index heterogeneous portions of corresponding planar lenses 23.sub.1 to 23.sub.4. These attempts are disclosed in E. W. Marchand, Gradient Index Optics, pp.7-21, Academic Press; K. Iga, Y. Kokubun, and M. Oikawa, Fundamentals of Micoroptics, pp.196-207, Academic Press; Y. Koike, Y. Sumi, and Y. Ohtuska, Applied Optics, Vol.25, No.19, pp.3356-3363(1986); and Japanese Patent Application Laying-open No. 101502/1989, for example.
As shown in FIG. 2, in the lens 12 the image is curved concave toward the lens 22 (negative curvature of image surface). On the other hand, as shown in FIG. 3, the compound lens 13 has an image positively curved. In both the compound lenses 12 and 13, resolution is therefore deteriorated.
In view of this, in Japanese Patent Application No. 84611/1991 the inventors have proposed a compound lens 14 as shown in FIG. 4. In this compound lens 14, the index distribution of each of the refractive index heterogeneous portions 23.sub.3 ' and 23.sub.4 ' of the second layer planar lens 23.sub.2 of the compound lens 13 in FIG. 3 is made to have an opposite gradient, and thereby curvature of image plane is corrected for enhancing resolution.
To produce a erecting image this compound lens 14 includes three lenses 21, 21 and 21 homogeneous in refractive index and four planar lenses 23.sub.1 to 23.sub.4 having an axial index distribution. The compound lens 14 has drawbacks below. (i) the planar lenses have a large number (six) of spherical surfaces. (ii) the length of the lens is large as compared to the diameter of the sphere lenses. (iii) The three refractive index homogeneous sphere lenses 21, 21, and 21 are higher in refractive index than the planar lenses 23.sub.1 to 23.sub.4, and therefore each of the terms of an equation showing Petzval's theorem has positive sign, with the result that remained curvature of image field is still large although aberration can be corrected.
In Fourier transform lenses and camera lenses which have different purposes, images may be inverted, and the above disadvantages (i) and (ii) are therefore overcome to some extent. However, the entrance side and exit sides of these optical systems are asymmetrical, and therefore (iv) another problem of correcting distortion is produced.
In coupling lenses used for coupling optical fibers, the input and output sides of the optical systems are arranged symmetrically to each other, and therefore distortion is corrected. However, in the case where a large number of optical fibers are arranged in the input and output sides of these lenses, (v) it is still another problem to arrange optical fibers, which are away from the optical axis, in parallel with the latter. In conventional optical systems using a sphere lens, a drop in efficiency is produced unless the optical fibers are directed so that they are arranged at angular intervals about the center of the sphere lens.
To facilitate understanding of the present invention, improvement in curvature of image field which is stated in the compound lens 14 will be generally discussed. The general relational equations about tertiary aberration are EQU MER. CURV.=-(3III+P) (2) EQU SAG. CURV.=-(III+P) (3)
In the equations, MER. CURV. represents a curvature of the tangential image surface, SAG. CURV. a curvature of sagital image surface, III a astigmatism coefficient, and P a Petzval sum.
Here, we study a sphere lens having a spherically symmetrical index distribution with a reduced spherical aberration. In this sphere lens, a light beam which is emitted from a point is focused on another point, and the astigmatism coefficient III is 0. By substituting III=0 to the equations (2) and (3), we have EQU MER. CURV.=SAG. CURV.=-P (4)
In the case of P.noteq.0, the best curvature of field of sphere lenses becomes a half of the absolute value of the curvature of field of a spherically symmetric sphere lens since the equation (5) is obtained from equations (2) and (3) if the astigmatism coefficient III=-P/2 by some means. EQU MER. CURV.=-SAG. CURV.=P/2 (5)
That is, the resolution substantially becomes double.
In such a manner, the curvatures of the tangential image surface and the curvature of sagital image surface may be balanced. However, in the conventional compound lenses except the compound lens 14 it is not possible to control astigmatism coefficient III with ease. Accordingly, it is an object of the present invention to establish controlling of astigmatism coefficient in lenses which are different in purpose and configuration from the compound lens 14.
Next, a problem of the present invention about distortion will be described in detail. In a camera lens, distortion becomes 0% if an image of a grating pattern object is formed similarly. In other words, if a height of an image at an image point of an incident light beam of which principal ray forms an angle of .omega. with the optical axis of the lens is in proportion with tan.omega., distortion becomes zero.
When in a Fourier transform lens, parallel rays of a wavelength .lambda. are incident on a diffraction grating having an grating pitch and located at a focus on the object side, a direction of m-th diffraction is given by the equation (6).
The spatial frequency is in proportion with 1/d, and therefore the distortion is eliminated if the height of an image is proportionate to sin.omega..
In f.omega. lens (usually called f.theta.), the height of an image may be in proportion with .omega..
As described above, distortion of compound lenses has different definitions according to objects of use.
Another object of the present invention is to provide a compound lens which has the same construction with the same index distribution for various uses, and which is capable of correcting distortion of the lens for various uses by modifying a small part of parameters thereof.